example 24.44 Linear and angular momentum

open in the book · parts/03-classical-mechanics/07-symplectic-geometry.tex:1468 · p. 866

example -- no derivation owed by its kind

Rests on

depends_on definition 24.43 Momentum map ¶
- depends_on definition 14.2 Lie group ¶
- depends_on definition 24.14 Hamiltonian vector field ¶
  - depends_on definition 24.8 Symplectic manifold ¶
    - depends_on definition 13.105 Closed form ¶
      - depends_on definition 13.103 Exterior derivative ¶
      - depends_on definition 13.98 $k$-form ¶
    - depends_on definition 13.98 $k$-form ¶ ↺
    - depends_on definition 24.2 Symplectic vector space ¶
      - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
  - depends_on equation 22.4 eq:ham-pdot ¶
  - depends_on equation 22.3 eq:ham-qdot ¶
- depends_on definition 24.17 Symplectomorphism ¶
  - depends_on definition A.70 Pullback ¶
    - depends_on definition 7.97 Partial derivative; gradient ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 5.15 Basis ¶
    - depends_on definition 13.83 Covector ¶
      - depends_on definition 13.81 Vector on a manifold ¶
    - depends_on definition 13.98 $k$-form ¶ ↺
  - depends_on definition 24.8 Symplectic manifold ¶ ↺
depends_on equation 24.3 eq:sym-canonical-forms ¶

Supports

depends_on example A.572 Rotational reduction of the central-force problem ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Momentum map	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1500
`depends_on`	→	eq:sym-canonical-forms	declared	parts/03-classical-mechanics/07-symplectic-geometry.tex:1500
`depends_on`	←	Rotational reduction of the central-force problem	declared	appendices/A-long-proofs.tex:27509